A logarithm is an exponent (power) to which a base
number must be raised to yield the same result. The
standard logarithm scale is called base 10.
The term "log" is used when specifying a log scale.

In base 10, the log of 100 = 2:

When basing your equation on base 10, indicating
the base is not required as base 10 is implied:

Other bases can be used, such as base 2, or base
3, or even base 25:

The reason for using a log scale is so we can
evaluate our data easier. For example, a chart of
data can either look like a boring straight line, or
with a log system applied, a more dynamic chart is
created:

The graph above is nothing in particular, but the
blue line will be raw data, and the pink line will
be the same data using a base 10 log scale.

This diagram is an example of a
Hertzsprung-Russell
Diagram (H-R diagram). Astronomers already have the
data in log form, so an example of an
H-R diagram
with just raw data only is hard to find, but the
dots will reside in the lower half of the graph and
the curves will not be apparent.